Convergent Economic Model Predictive Control through parameter-varying storage functions for dissipativity

TL;DR

This paper introduces a novel economic model predictive control framework utilizing parameter-varying storage functions to ensure dissipativity and convergence without standard assumptions, demonstrated through an illustrative example.

Contribution

It extends dissipativity to parameter-varying storage functions within EMPC and formulates controllers that guarantee recursive feasibility and convergence.

Findings

Ensures recursive feasibility of EMPC with parameter-varying storage functions.

Achieves asymptotic convergence to optimal equilibrium without standard dissipativity.

Provides bounds on asymptotic average closed-loop performance.

Abstract

This paper presents a new concept of controlled dissipativity as an extension of the standard dissipativity property to systems with parameter-varying storage functions under the framework of economic model predictive control (EMPC). Based on this concept, two EMPC controllers, integrated with the dissipation inequality constraints rendering the storage function parameters as decision variables, are formulated and the associated recursive feasibility is ensured. Then, the asymptotic convergence to an optimal equilibrium in closed-loop, without requiring the standard dissipativity assumption, is enforced by trading it off with asymptotic performance. The upper bound of asymptotic average closed-loop performance is also evaluated. Finally, an illustrative example by using the EMPC controllers with terminal equilibrium or terminal region conditions is provided to show the effectiveness of our methods.